The rule is to use whatever amount of chlorine is needed to maintain a minimum Free Chlorine (FC) level relative to the Cyanuric Acid (CYA) level. How often you need to add chlorine depends on the type of chlorine you are using since some forms are slow dissolving, such as Trichlor tabs/pucks, while others are immediate, such as chlorinating liquid or unscented bleach.

If you use stabilized chlorine (Trichlor or Dichlor) then you may build up CYA in which case you'll probably need to use an algaecide (PolyQuat 60 or a phosphate remover) to prevent algae growth. You can prevent algae using chlorine alone, but it requires you to increase the FC level as the CYA level rises and that's hard to do using stabilized chlorine.

If you consistently maintain an appropriate chlorine level, then you normally do not need to shock except from heavy bather loads or other one-time events (storms, etc.).

You should absolutely, positively NOT use PoolBrand 3" Chlorinating Tablets in your skimmer. When the pump goes off, the tablets continue to slowly dissolve and are VERY acidic. This can damage the area of your pool near the skimmer as well as rust any metal in the skimmer including thermometers and the blast of acid when the pump starts up will not be good for the metal in your heater, or your pump seals, or your filter (depending on type). Most Trichlor tabs/pucks are designed to be used in a floating feeder or an in-line chlorinator. They are NOT to be put in the skimmer.

There are some specialized Trichlor tabs called BioGuard Smart Sticks that stop dissolving when there is no water flow so can be used in the skimmer.

However, if you use any of these Trichlor tabs/pucks, then your Cyanuric Acid (CYA) level will likely continue to rise unless you dilute your pool water regularly. So you'll need to use a supplemental algaecide if the CYA level rises, such as a weekly dose of PolyQuat 60 or a phosphate remover. Plus the acidity of the Trichlor will require you to use pH Up (or possibly Borax) to maintain the pH and all of these products are costly -- much more than the Trichlor by itself.

An alternative to this is to use chlorinating liquid or unscented bleach (Clorox Regular or off-brand Ultra), but this requires daily or every other day chlorine addition. If you have a good pool cover that keeps the UV rays of sunlight off the pool, then you can perhaps add chlorine twice a week. If you want to automate the addition of chlorinating liquid or bleach, then you can use The Liquidator which is talked about in this thread.

In any event, you should get yourself a good test kit -- either the Taylor K-2006 you can get at a good online price here or the TF100 test kit from tftestkits(dot)com here with the latter having 36% more volume of reagents so is comparably priced "per test".